Related papers: A Solution to Galileo's Enigma "Mostro Son Io"
The Monty Hall puzzle has been solved and dissected in many ways, but always using probabilistic arguments, so it is considered a probability puzzle. In this paper the puzzle is set up as an orthodox statistical problem involving an unknown…
The usual modelling of the syllogisms of the Organon by a calculus of classes does not include relations. Aristotle may however have envisioned them in the first two books as the category of relatives, where he allowed them to compose with…
In this short article, we look at an old logical puzzle, its solution and proof and discuss some interesting aspects concerning its representation in a logic programming language like Prolog. We also discuss an intriguing information…
We analyze the geometrical structure of the astonishing Nasca geoglyphs in terms of their fractal dimension with the idea of dating these manifestations of human cultural engagements in relation to one another. Our findings suggest that the…
In this paper, a Gauss-Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to a system of linear equations, where the coefficient matrix may be full rank or rank deficient and the system is…
Since techniques used to address the Nivat's conjecture usually relies on Morse-Hedlund Theorem, an improved version of this classical result may mean a new step towards a proof for the conjecture. In this paper, considering an alphabetical…
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
Benoit Mandelbrot's scientific legacy spans an extraordinary range of disciplines, from linguistics and fluid turbulence to cosmology and finance, suggesting the intellectual temperament of a "fox" in Isaiah Berlin's famous dichotomy of…
In a recent paper, Caracciolo, Sokal and Sportiello presented, inter alia, an algebraic/combinatorial proof for Cayley's identity. The purpose of the present paper is to give a "purely combinatorial" proof for this identity; i.e., a proof…
This exposition reviews what exactly Gauss asserted and what did he prove in the last chapter of {\sl Disquisitiones Arithmeticae} about dividing the circle into a given number of equal parts. In other words, what did Gauss claim and…
In 2023, H.\,Brezis published a list of his ``favorite open problems", which he described as challenges he had ``raised throughout his career and has resisted so far". We provide a complete resolution to the first one--Open Problem 1.1--in…
In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of…
Following a conjecture of Feynman, we explore the possibility that only those energy forms that are associated with (massive or massless) particles couple to the gravitational field, but not others. We propose an experiment to deflect…
We introduce Aristotle, an AI system that combines formal verification with informal reasoning, achieving gold-medal-equivalent performance on the 2025 International Mathematical Olympiad problems. Aristotle integrates three main…
D\'ungal's letter to Charlemagne on the double solar eclipse in the year 810 is extremely interesting both for its form and for its subject matter. Part I of the present study deals with the epistula as a literary work (genre, language,…
Goedel Incompleteness Theorem leaves open a way around it, vaguely perceived for a long time but not clearly identified. (Thus, Goedel believed informal arguments can answer any math question.) Closing this loophole does not seem obvious…
The sine-Gordon equation is a nonlinear partial differential equation. It is known that the sine-Gordon has soliton solutions in the 1D and 2D cases, but such solutions are not known to exist in the 3D case. Several numerical solutions to…
This document summarizes the proofs made during a Coq development inSummer 2015. This development investigates the function G introducedby Hofstadter in his famous "G{\"o}del, Escher, Bach" bookas well as a related infinite tree. The…
The poem Helen of the Nobel laureate George Seferis was inspired by the anti war play Helen of Euripides. In his poem, Seferis empathizes with the hero of the tragedy, Teucer, who opposed the involvement of The Gods in the lives of the…
In this paper, we introduce a novel identity for generalized Euler polynomials, leading to further generalizations for several relations involving classical Euler numbers, Euler polynomials, Genocchi polynomials, and Genocchi numbers.